A better beak? (5)

I believe the answer is:

finer

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'a better' is the definition.
(I've seen this in another clue)

I can't explain the rest of the clue.

(Other definitions for finer that I've seen before include "Better; more slender" , "Better quality" , "More thin, excellent" , "More gossamer or splendid" , "'Nothing could be . . . . . than to be in Carolina, in the morning' (popular song)" .)

I've seen this clue in the Evening Standard.

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